Yes, but please first provide some more information: What will be the purpose of your blog? Will it be primarily text with some images, mostly images with some text, or an even mix? Do you want a blog that you create from scratch or one whose host makes it really easy to create a blog? Blogger and Wordpress are probably the two most commonly-used hosts, if you want to check them out, but there are others, too. Feel free to PM me if you prefer.

A rather late response from me. I have a free blog at Livejournal which I started roughly 5 years ago. It allows you (for the time being - they're trying to change things) to have your own layout and stuff plus you can join up with various groups/communities. A couple of days ago I set one up with WordPress, which I also really like. It takes some to figure out what is what and what goes where but once you've got the hang of it, you can quickly make a website that looks really professional. :)